Conference Paper

Exploiting Monge Structures in Optimum Subwindow Search

Dept. of Comput., Curtin Univ. of Technol., Perth, WA, Australia
DOI: 10.1109/CVPR.2010.5540119 Conference: Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on
Source: IEEE Xplore


Optimum subwindow search for object detection aims to find a subwindow so that the contained subimage is most similar to the query object. This problem can be formulated as a four dimensional (4D) maximum entry search problem wherein each entry corresponds to the quality score of the subimage contained in a subwindow. For n × n images, a naive exhaustive search requires O(n4) sequential computations of the quality scores for all subwindows. To reduce the time complexity, we prove that, for some typical similarity functions like Euclidian metric, χ2 metric on image histograms, the associated 4D array carries some Monge structures and we utilise these properties to speed up the optimum subwindow search and the time complexity is reduced to O(n3). Furthermore, we propose a locally optimal alternating column and row search method with typical quadratic time complexity O(n2). Experiments on PASCAL VOC 2006 demonstrate that the alternating method is significantly faster than the well known efficient subwindow search (ESS) method whilst the performance loss due to local maxima problem is negligible.

Download full-text


Available from: Wanquan Liu, Mar 10, 2014
  • Source
    • "Recently, Efficient Subwindow Search (ESS) [3] was proposed to efficiently find the global optimal subwindow. Furthermore, the computational complexity of ESS has a wide variance across the image and its worst case computational complexity is O(n 4 ) [10]. To further reduce computational complexity, improved ESS (I-ESS) [4] and Alternating ESS (A-ESS) [4] were proposed. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we propose a Partial Least Squares based sub-window search method for pedestrian detection, by which the detection speed can be improved effectively while maintaining high detection accuracy. Firstly, a sparse search is implemented to find all the possible locations containing parts of a pedestrian. Then a pre-learned Partial Least Squares regression model is applied to estimate the displacements of the subwindows to guide them towards the approximate locations of the pedestrians. Finally, we conduct a dense search around the approximate locations to obtain the exact locations of the pedestrians. Experiments on the INRIA dataset demonstrate that our method greatly reduces the number of search windows, which leads to much fewer feature extraction in the detection phase. Thus, it is about 10 times faster than the sliding window method with a jump step of 8 × 8.
    Preview · Conference Paper · Jan 2011
  • Source
    • "The task of object detection is to find a subwindow í µí±¤ so that í µí±“ (s í µí±¤ ) is maximum, that is max í µí±¤∈í µí²² í µí±“ (s í µí±¤ ) (1) where í µí²² is the set of all possible subwindows, i.e., í µí²² = {í µí±¤ = [í µí±¡ : í µí±, í µí±™ : í µí±Ÿ]∣1 ≤ í µí±¡ ≤ í µí± ≤ í µí±›, 1 ≤ í µí±™ ≤ í µí±Ÿ ≤ í µí±›}. (2) Now let us define a 4D array í µí°´, similar to that in [3], í µí°´[í µí±¡, í µí±, í µí±™, í µí±Ÿ] = { í µí±“ (s í µí±¤ ); if í µí±¤ = [í µí±¡ : í µí±, í µí±™ : í µí±Ÿ] ∈ í µí²² −∞, otherwise (3) "
    [Show abstract] [Hide abstract]
    ABSTRACT: Subwindow search aims to find the optimal subimage which maximizes the score function of an object to be detected. After the development of the branch and bound (B&B) method called Efficient Subwindow Search (ESS), several algorithms (IESS [2], AESS [2], ARCS [3]) have been proposed to improve the performance of ESS. For �� ×�� images, IESS’s time complexity is bounded by �� (�� 3 ) which is better than ESS, but only applicable to linear score functions. Other work shows that Monge properties can hold in subwindow search and can be used to speed up the search to �� (�� 3 ), but only applies to certain types of score functions. In this paper we explore the connection between submodular functions and the Monge property, and prove that submodular score functions can be used to achieve �� (�� 3 ) time complexity for object detection. The time complexity can be further improved to be sub-cubic by applying B&B methods on row interval only, when the score function has a multivariate submodular bound function. Conditions for submodularity of common non-linear score functions and multivariate submodularity of their bound functions are also provided, and experiments are provided to compare the proposed approach against ESS and ARCS for object detection with some nonlinear score functions.
    Full-text · Conference Paper · Jan 2011
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper addresses the performance improvement of efficient sub-window search algorithms for object detection. The current algorithms are for flexible rectangle-shaped sub-window with high computation costs. In this paper, a restriction is applied on the sub-window shape from rectangle into square in order to reduce the number of possible sub-windows with an expectation to improve the computation speed. However, this may come with a consequence of accuracy loss for some objects. In addition, another variance of sub-window shape is also tested which based on the ratio between the height and width of an image. The experiment results on the proposed algorithms were analysed and compared with the performance of the original algorithms to determine whether the speed improvement is significantly large while making the accuracy loss acceptable. It was found that some new algorithms show a good speed improvement while maintaining small accuracy loss. Furthermore, there is an algorithm designed from a combination of a new algorithm and an original algorithm which gains the benefit from both algorithms and produces the best performance among all new algorithms.
    No preview · Article · Feb 2012 · International Journal of Machine Learning and Cybernetics
Show more